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Characterizing robust optimal solution sets for nonconvex uncertain semi-infinite programming problems involving tangential subdifferentials

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Abstract

In this paper, we give some characterizations of the robust optimal solution set for nonconvex uncertain semi-infinite programming problems in terms of tangential subdifferentials. By using a new robust-type constraint qualification, we first obtain some necessary and sufficient optimality conditions of the robust optimal solution for the nonconvex uncertain semi-infinite programming problem via the robust optimization approach. Then, by using the Dini pseudoconvexity, we obtain some characterizations of the robust optimal solution set for the nonconvex uncertain semi-infinite programming problem. Finally, as applications of our results, we derive some optimality conditions of the robust optimal solution and characterizations of the robust optimal solution set for the cone-constrained nonconvex uncertain optimization problem. Some examples are given to illustrate the advantage of the results.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, People’s Republic of China

    Juan Liu, Xian-Jun Long & Xiang-Kai Sun

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  1. Juan Liu
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  2. Xian-Jun Long
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  3. Xiang-Kai Sun
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Correspondence to Xian-Jun Long.

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This work was supported by the National Natural Science Foundation of China (11471059), the Basic and Advanced Research Project of Chongqing (cstc2021jcyj-msxmX0721), the Education Committee Project Research Foundation of Chongqing (KJZDK201900801, KJZDK202100803)

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Liu, J., Long, XJ. & Sun, XK. Characterizing robust optimal solution sets for nonconvex uncertain semi-infinite programming problems involving tangential subdifferentials. J Glob Optim 87, 481–501 (2023). https://doi.org/10.1007/s10898-022-01134-2

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  • DOI: https://doi.org/10.1007/s10898-022-01134-2

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